There is a huge literature on common misinterpretations and misconceptions surrounding the \(p\) -value.This debate is particularly heated because the null hypothesis significance test (NHST) is the standard procedure in many fields, including e.g. psychology or medicine. Here, a \(p\) -value smaller than 0.05 (which corresponds to \(1.96\sigma \)  in the Gaussian approximation) is enough to claim a “statistically significant" result; see Nickerson [1]} for a review of this debate and Wasserstein et al. [2]} for recent developments. Given that the NHST is less prominent in physics this debate gets only minor attention here. Obviously it is incorrect to interpret \(p\)  as the probability that \(H_0\)  is true, since \(p\)  is calculated under the assumption of \(H_0\)  being true (not to mention that the frequentist framework does not allow probability assignments to hypotheses). If we denote the observed data by \(D\)  (and more extreme data by \(D^*\) ) we may describe the \(p\) -value symbolically as a conditional probability, \(p=P(D^*|H_0)\) , which should not be confused with the inverse, i.e. \(p\ne P(H_0|D)\) . Hence, this misinterpretation has been called the inverse probability fallacy [3]}.
